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D.J. started taking marbles

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D.J. started taking marbles

by sanju09 » Sat Jul 10, 2010 6:02 am
There were twenty-one marbles in a bag. Seven marbles were green, seven were red, and seven were blue. D.J. started taking marbles out of the bag. He stopped when he had two marbles of the same color. How many marbles did he take out of the bag?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
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by grockit_andrea » Sat Jul 10, 2010 6:13 am
Well, if DJ got 2 marbles of the same color on the first try, he took out 2 marbles, and the answer would be A. If he got different colored marbles, for instance one green and one blue, then he would take out a third marble. If that marble were the same color as one of the previous marbles-- green or blue-- he would stop there, and the answer would be B. If DJ drew a marble of the third color, though (in this hypothetical, red) then he would have to draw a fourth marble. He would definitely stop there, because that marble would absolutely be one of the three colors, so no matter what, he would have two marbles of the same color, and the answer would be C. Unless I'm missing something, the question as stated can't be answered, because A, B, or C could be correct, depending on the circumstance. Where is this question from?
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by kvcpk » Sat Jul 10, 2010 6:17 am
Since there are only 3 colors, it would require maximum 4 marbles to be picked. mimimum is 2.
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by GMATGuruNY » Sat Jul 10, 2010 10:00 am
A better question:

A bag contains twenty-one marbles. Three of the marbles are green, ten are red, and seven are blue. What is the minimum number of marbles that would have to be removed from the bag in order to guarantee that at least one marble of every color is included among the removed marbles?

(A) 3
(B) 7
(C) 10
(D) 17
(E) 18
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by kvcpk » Sat Jul 10, 2010 10:14 am
GMATGuruNY wrote:A better question:

A bag contains twenty-one marbles. Three of the marbles are green, ten are red, and seven are blue. What is the minimum number of marbles that would have to be removed from the bag in order to guarantee that at least one marble of every color is included among the removed marbles?

(A) 3
(B) 7
(C) 10
(D) 17
(E) 18
Hi Mitch,

In the worst case scenario:
10 Red + seven Blue + 1 green
So 18 balls have to be removed.

Is that right?
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by GMATGuruNY » Sat Jul 10, 2010 10:16 am
kvcpk wrote:
GMATGuruNY wrote:A better question:

A bag contains twenty-one marbles. Three of the marbles are green, ten are red, and seven are blue. What is the minimum number of marbles that would have to be removed from the bag in order to guarantee that at least one marble of every color is included among the removed marbles?

(A) 3
(B) 7
(C) 10
(D) 17
(E) 18
Hi Mitch,

In the worst case scenario:
10 Red + seven Blue + 1 green
So 18 balls have to be removed.

Is that right?
Perfect! The trick is to determine -- as you did -- the worst case scenario.
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